YMSC-BIMSA Quantum Information Seminar

This talk aims to present recent applications of Quantum Computing in Geographic Information Science and related disciplines.1)Conformal Map Projection and Discrete Geometry based on Riemann Surface ; 2)some classical geo-computing work based on Google Earth Engine and Earth System Model; 3)Quantum computing applied to the Earth System Model and Climate Change based on High-performance cluster simulation.

Bio:

Yi Liu（刘熠） is a postdoc at BIMSA. His main research interests are Quantum Computation, Cartography and Earth System Model(Land model-DGVM/GGCM).He visited Munich University of Technology and Potsdam Institute for Climate Impact Research, and participated in the field Investigations of the Siberian Railway and Baikal Lake. Dr Liu graduated with a PhD in Cartography and Geographical Information System from State Key Laboratory of Resources and Environmental Information Systems，the Chinese Academy of Science.

As one of the key properties that distinguish quantum mechanics from the classical one, entanglement lies at the center of quantum information technology and science. The success of many quantum information tasks, including quantum key distribution, quantum metrology, and quantum teleportation, highly depends on the generation of high-fidelity entangled states. Therefore, developing efficient and effective protocols to detect entanglement in real-world systems has practical significance and benefits theoretical studies. In this talk, I will first introduce the definition of entanglement and some commonly-used entanglement detection protocols, like entanglement witness and positive map criteria. Then I will review some of our recent works about entanglement detection, in which we designed many practical entanglement detection protocols and proposed a fundamental limitation regarding the cost of entanglement detection.

马雄峰Xiongfeng Ma is an associate professor at the Institute for Interdisciplinary Information Sciences, Tsinghua University. His main research interest lies in quantum information science, including quantum cryptography and quantum foundation. After obtaining his BSc at Peking University in 2003, Xiongfeng attended the University of Toronto for his PhD degree. From 2008 to 2011, he did his post-doc and visiting positions at the University of Waterloo, the University of Toronto, and the University of Leeds. In 2012, Xiongfeng joined Tsinghua University.

量子计算机能否被建造出来，如果原理上可以的话它的建造难度是什么？这个问题背后的核心是：量子系统如何抗噪。为了实现量子计算的抗噪，我们一般从几个方面来考虑：1）量子硬件的制备和实验提升，2）量子系统的控制方法，3）容错性量子计算的算法软件的构建。本报告将会对后面两个问题进行阐述，并且试图从理论层面提出新的科学问题。

首先我们讨论一下量子计算机的核心控制部分—校准系统。当量子芯片的比特数目变大并且量子运算更加复杂时，各个比特之间不可避免的有相互影响，导致操控变得复杂。同时受环境和器件影响，比特的参数会随时间漂移从而影响操控和测量，导致量子计算出现严重错误。因此，如何实现量子芯片的自动控制和实时维护是实现量子计算的核心。我们将重点讨论并且提出量子计算机校准控制中的科学问题。

其次，量子纠错编码是实现通用容错量子计算的一个重要方案。我们发现表面码在测量诱导的相干错误下会产生不能被探测到的错误，这些错误将累积并演变为逻辑错误。这种现实上可能出现的重要错误会使量子码变成“近似”量子纠错码，这种效应会使量子纠错程序在更多次循环后变得非常有害。考虑到容错量子计算的实现复杂度和理论上的问题。但是，我们的结果表明：通过增加量子编码的尺度可以显著的减小这种危害性。近期量子计算中需要尽可能考虑复杂度较低的针对特定问题设计的抗噪量子算法。最后，我们介绍一个基于随机编译方案的抗噪量子相位估计算法的设计和原理。

刘东副教授于2018年5月加入清华大学物理系，在2020年加入北京量子信息研究院成为兼任研究员，并且负责“量子操作系统”团队。他分别于2005、2012年在北京大学和杜克大学获得学士和博士学位，之后在密西根州立大学和微软研究院Station Q从事博士后研究，并且在2018年入选某海外高层次青年人才计划。刘东课题组近五年主要致力于拓扑量子器件的验证方案、量子计算机的体系结构、非平衡多体量子物理的量子场论方法等方向的理论研究。

Entanglement detection is essential in quantum information science and quantum many-body physics. It has been proved that entanglement exists almost surely for a random quantum state, while the realizations of effective entanglement criteria usually consume exponential resources, and efficient criteria often perform poorly without prior knowledge. This fact implies a fundamental limitation might exist in the detectability of entanglement. In this work, we formalize this limitation as a fundamental trade-off between the efficiency and effectiveness of entanglement criteria via a systematic method to theoretically evaluate the detection capability of entanglement criteria. For a system coupled to an environment, we prove that any entanglement criterion needs exponentially many observables to detect the entanglement effectively when restricted to single-copy operations. Otherwise, the detection capability of the criterion will decay double-exponentially. Furthermore, if multi-copy joint measurements are allowed, the effectiveness of entanglement detection can be exponentially improved, which implies a quantum advantage in entanglement detection problems.

(Ref: Pengyu Liu, Zhenhuan Liu, Shu Chen, Xiongfeng Ma. arXiv:2208.02518)

雍熙，水利部信息中心高级工程师。

量子霸权的概念一提出便引发了各方面的争论，这些争议有来自科学内部共同体的，也有来自社会大众的。目前验证量子霸权的实验方案中最受关注的有随机量子电路采样和玻色采样，量子霸权相关实验引发了包括用于对照的经典算法选择的合理性、量子计算结果的准确性以及“Quantum Supremacy”用词合理性的多方面争议。从计算复杂性理论的角度来看，量子计算超越经典计算可否最终实现仍然没有定论。与此同时，“悬铃木”和“九章”等实现量子霸权的物理实验在争议中展示出不间断的科学进步。量子霸权相关的科学争论充分展现了现代科技本身深刻性和复杂性，尤其在传媒时代，公众的参与进一步加剧了这种复杂性。

离子，即带电的原子，是最早被应用于量子计算的平台之一。近些年来离子阱量子计算在国际上得到了广泛的关注和显著的进展：学术界之外，在美国和欧洲的工业界也引起了广泛兴趣，可以操纵任意连通的30多个比特，进行高保真度量子逻辑门与量子态探测。

在这个讲座中，我将介绍离子量子比特的工作原理：用完美的（带电）原子来编码量子信息，并用激光进行高保真度操控。在此基础上我们实现了53个量子比特的量子模拟，研究非平衡态演化过程，接近经典计算的极限。我们将这类方法扩展，把量子比特编码在高维的非欧空间里，并在未来期待实现可验证的量子采样与量子纠错。

Quantum error-correcting codes (QECCs) are believed to be a necessity for large-scale fault-tolerant quantum computation. In the past two decades, various methods of QECC constructions have been developed, leading to many good families of codes. However, the majority of these codes are not suitable for near-term quantum devices. Here we present VarQEC, a noise-resilient variational quantum algorithm to search for quantum codes with a hardware-efficient encoding circuit. Given the target noise channel (or the target code parameters) and the hardware connectivity graph, we optimize a shallow variational quantum circuit to prepare the basis states of an eligible code. We have verified its effectiveness by (re)discovering some symmetric and asymmetric codes, e.g., ((n,2n−6,3))2 for n from 7 to 14. We also found new ((6,2,3))2 and ((7,2,3))2 codes that are not equivalent to any stabilizer code, and extensive numerical evidence with VarQEC suggests that a ((7,3,3))2 code does not exist. Furthermore, we found many new channel-adaptive codes for error models involving nearest-neighbor correlated errors. Our work sheds new light on the understanding of QECC in general, which may also help to enhance near-term device performance with channel-adaptive error-correcting codes.

题目：寻找量子纠错码的量子变分算法

摘要： 为了实现大规模容错量子计算，我们必须有探测和纠正噪声的手段——量子纠错。在过去的二十年里，人们构造了一系列不同的量子纠错码，但其中的绝大部分并不适用于近期量子设备。在这个报告里，我们介绍一个用于寻找量子纠错码的量子变分算法。给定目标量子噪声信道和硬件的连接方式，我们优化对应的量子变分线路，可以找到信道自适应的量子纠错码，而优化后的线路即为其编码线路。通过数值优化，我们找到了一系列已知的量子纠错码，如((5,2,3)),((7,2,3)),((10,4,4)),((14,256,3))，还找到了一系列新的信道自适应的量子纠错码。我们的算法通过近期量子计算机寻找纠错码，反过来，这些纠错码也有望提高近期量子计算机的表现。

报告人：曹晨风，香港科技大学博士生，2019年本科毕业于中国科学院大学。研究兴趣为量子信息和量子计算，重点关注近期量子算法和量子纠错。有数篇工作发表于Physics Review Applied/Research 等物理期刊，多次在AQIS等量子计算会议做口头报告，长期担任PRX Quantum, Quantum, New Journal of Physics 等期刊和QIP会议审稿人。

Geometric and holonomic quantum computation utilizes intrinsic geometric properties of quantum-mechanical state spaces to realize quantum logic gates. Since both geometric phases and quantum holonomies are global quantities depending only on the evolution paths of quantum systems, quantum gates based on them possess built-in resilience to certain kinds of errors. This talk provides an introduction to the topic as well as gives an overview of the theoretical and experimental progress for constructing geometric and holonomic quantum gates.

Bio:

Jiang Zhang is an assistant professor in the quantum algorithm group of Beijing Academy of Quantum Information Sciences (BAQIS). He received his Ph.D degree from Shandong University in 2015. Then he worked at Beijing Computational Science Research Center (CSRC) and Tsinghua University as a postdoctoral fellow. Before joining BAQIS in 2020, he was an assistant professor at Pengcheng Laboratory (PCL) in Shenzhen. His research interests lie in holonomic quantum computation, dynamical decoupling, quantum error correction, and quantum algorithms.

Ref: arxiv.org/abs/2110.03602

Construct the world of topological quantum matter

——From quantum anomalous Hall system to topological superconductor

Ke He

- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China

- Beijing Academy of Quantum Information Sciences, Beijing 100193, China

The discoveries of the integer and fractional quantum Hall effects in early 1980s unveiled a class of quantum states of matter and effects induced by non-trivial topological properties in the electronic structure of materials. A large family of topological states of matter have been conceived after that, not only promoting our understanding on condensed matter but providing solutions to low-energy-consumption electronics and error-tolerant quantum computation. How to achieve the theoretically predicted exotic quantum states of matter in the real world is a major challenge in the field. Many novel topological states of matter are obtained from simple “top models”, which implies the possibility of constructing the states of matter in a “bottom-up” manner. In this talk, I will introduce our studies based on this idea—trying to realizing some novel topological states of matter and effect by designing, constructing and engineering materials and heterostructures with atomically accurate fabrication and characterization techniques such as molecular beam epitaxy and angle-resolved photoemission spectroscopy. I will mainly introduce our works on the quantum anomalous Hall effect in magnetic topological insulators and our recent exploration on a new nanowire-based topological superconductor.

上世纪80年代整数和分数量子霍尔效应的相继发现使人们认识到利用物质电子结构的拓扑性质可以实现一些新奇的物态以及量子效应。此后人们构想出了丰富多彩的拓扑量子物态，不但大大加深了对物质科学的理解，还对低能耗电子器件、容错量子计算等方面的问题提供了新的解决方案。如何在真实的世界中实现理论构想的拓扑量子物态一直是此领域研究的一大难题。很多有趣的拓扑量子物态可以通过简洁的“玩具”模型获得，这使得在实验上以“自下而上”的方式构筑这些物态成为可能。在此报告中，我将介绍我们结合分子束外延、角分辨光电能谱等高精度的材料制备、表征技术，通过对材料结构的设计、构筑与调控，实现拓扑量子物态和效应的相关研究，主要包括磁性拓扑绝缘体中量子反常霍尔效应的实现与调控，以及近期对一种新的拓扑超导纳米线系统的探索。

何珂，清华物理系教授，低维量子物理国家重点实验室，北京量子信息科学研究院。中国科学院杰出科技成就集体奖（2011）、中国青年科技奖（2013 年）、日本仁科亚洲奖（2015）、叶企孙物理奖（2017）、国家自然科学一等奖（2018）Email: kehe@tsinghua.edu.cn

This report begins with a brief introduction to the background of quantum computing and the history of quantum algorithms. Then introduce the linear combinations of unitary operators (LCU), which can expand the Hilbert space and transform the classical algorithms into quantum version conveniently. Then, it focuses on the applications of quantum algorithms in chemical simulation, differential equations, which suffers a high complexity in computing.

本报告首先简要介绍量子计算的背景知识以及量子算法的历史。随后介绍幺正算符线性叠加（LCU）算法框架，采用该框架能扩展希尔伯特空间，可方便的将经典算法量子化。随后重点介绍量子算法在化学模拟、微分方程组等高复杂度领域的应用以及实验实现。

魏世杰，北京量子信息研究院助理研究员，副高级职称。于2014年进入清华大学物理系攻读博士学位，目前研究方向为量子计算理论，专注于量子算法的构造与创新。（weisj@baqis.ac.cn）

Near-term quantum machines provide a novel way to explore many scientfic domains beyond the reach of classical machines. Meanwhile, near-term quantum machines are fragile, where the available quantum resources are limited and error-prone. Variational quantum algorithms (VQAs) are leading candidates to alleviate these defects. Experimental studies have demonstrated the potential of VQAs in a plethora of areas including machine learning, fundamental science, and quantum chemisty. Neverthess, theoretical understanding of VQAs remains largely unknown. To address this issue, in this talk, we investigate the expressivity of VQAs through the lens of statistical learning theory. According to the entangled relation between expressivity and model power, we further utilize the achieved results to analyze the generalization ability of a wide class of quantum discriminative and generative learning models and discuss potential advantages.

Bio

Yuxuan Du is currently a Senior Researcher at JD Explore Academy, and also a member of Doctor Management Trainee at JD. com. Prior to that, he received a Ph.D. degree in computer science from The University of Sydney and a Bachelor of Physics (elite class) from Sichuan University. His research interests include fundamental algorithms for quantum machine learning, quantum learning theory, and quantum computing. He has published his research outcomes in many top-tier journals and conferences in physics and computer science including Physical Review Letters, Physical Review X Quantum, npj Quantum Information, Transactions on Information Theory, Conference on Computer Vision and Pattern Recognition, etc.

We give a characterization of a finite-dimensional commuting square of C*-algebras that produces a hyperfinite type II_1 subfactor of finite index and finite depth in terms of Morita equivalent unitary fusion categories. This type of commuting squares were studied by N. Sato, and we show that a slight generalization of his construction covers the fully general case of such commuting squares. We also give a characterization of such a commuting square that produces a given hyperfinite type II_1

subfactor of finite index and finite depth.

Tensor codes provide a simple family of combinatorial constructions of locally testable codes that generalize the family of Reed-Muller codes. The natural test for tensor codes, the axis-parallel line vs. point test, plays an essential role in constructions of probabilistically checkable proofs. The quantum soundness of tensor code test is an essential component of the MIP* = RE theorem as it naturally generalize the low indivitual degree test. In this talk, we will discuss the proof ideas behind the quantum soundness analysis, its use in the MIP* = RE proof, and several interesting related open problems.

Bio: Zhengfeng Ji is currently a professor in the Department of Computer Science and Technology, Tsinghua University. His research studies quantum computing from a computer science perspective, recently focusing on the quantum algorithm and complexity theory, quantum cryptography, and quantum software.